Odo has the same excuse as Data - both have superior strength and much better motor control than most humanoids, Odo has talked about how his body works and how humanoid bodies are put together almost as if its a hobby.
It's clearly just a pressure point, nothing requiring touch telepathy as Nimoy originally stated. On Voyager, the Doctor even managed to detect the nerve trauma from a botched pinch.
It's never made entirely clear why it's so difficult for non-Vulcans to do it if it doesn't involve telepathy. For that matter, it's never really made clear why it works at all - several human martial arts are well aware of pressure points in the shoulder, but none of them can cause unconsciousness, only extreme pain and temporary (often less temporary) paralysis.
Another thing to consider is "Why does it work on most races?"
Obviously you don't need to be telepathic. It apparently requires knowledge of the target's anatomy, precise motor control, and physical strength. But... do all races have a vulnerable point?